The following is a full list of all my articles, available as pdf files.

- The alternating algorithm in a uniformly convex and uniformly smooth
Banach space,
*Journal of Mathematical Analysis and Applications***421**(2015), 747-753. [[pdf]]. This article may be viewed at Science Direct. - (with G. Kutyniok, H. Rauhut and V. Temlyakov), Preface to the
Special Issue on Sparse Approximate Solution of Linear Systems, in
*Lin. Alg. Appl.***441**(2014), 1-3. [[pdf]]. This preface may be viewed at Science Direct. - Smoothness and Uniqueness in Ridge Function Representation,
*Indagationes Mathematicae***24**(2013), 725-738. [[pdf]]. This article may be viewed at Science Direct. See errata. - (with V. E. Ismailov) Interpolation on Lines by Ridge
Functions,
*Journal of Approximation Theory***175**(2013), 91-113. [[pdf]]. This article may be viewed at Science Direct. - On Ridge Functions,
*Azerbaijan Journal of Mathematics***3**(2013), 122-130. [[pdf]]. - (with A. Kroó) On Stability of the Metric Projection Operator,
*SIAM J. Math. Analysis***45**(2013), 639-661. [[pdf]]. This article may be viewed at SIAM Journal on Mathematical Analysis. - On Best Rank
*n*Matrix Approximations,*Linear Algebra and its Applications***437**(2012), 2179-2199. [[pdf]]. This article may be viewed at Science Direct. - (with Y. Benyamini and A. Kroó)
*L*–Approximation and Finding Solutions with Small Support,^{1}*Constructive Approximation***36**(2012), 399-431. [[pdf]]. This article can be viewed at Springer. - (with J.M. Quesada) On Chebyshev-Markov-Krein Inequalities,
*Journal of Approximation Theory***164**(2012), 1262-1282. [[pdf]]. This article may be viewed at Science Direct. - Sparse Representations and Approximation
Theory,
*Journal of Approximation Theory***163**(2011), 388-412 [[pdf]]. This article may be viewed at Science Direct. - (edited with A. Kroó and Y. Xu) In Memoriam Borislav D.
Bojanov: 18 November 1944–8 April 2009,
*Journal of Approximation Theory***162**(2010), 1739-1765 [[pdf]]. This article may be viewed at Science Direct. - (with R. Pinchasi) Dominating Subsets under Projections,
*SIAM J. Discrete Math.***24**(2010), 910–920 [[pdf]]. This article may be viewed directly from SIDMA. Review from Zentralblatt. - (with A. Kroó) Strong Uniqueness,
*Surveys in Approximation Theory***5**(2010), 1-91. [[pdf], [ps]] and Surveys in Approximation Theory. Review from MR. - Zero Minors of Totally Positive Matrices,
*Electronic Journal in Linear Algebra***17**(2008), 532-542. [[pdf]]. This article may be viewed directly from ELA. - (with D. Hershkowitz) On Nonnegative Sign Equivalent and Sign Similar
Factorizations of Matrices,
*Electronic Journal in Linear Algebra***16**(2007), 162-170. [[pdf]]. This article may be viewed directly from ELA. Review from Zentralblatt. - (with D. Wulbert) Extending
*n*-Convex Functions,*Studia Math.***171**(2005), 125-152. [[pdf]]. Review from MR. - (with E. L. Ortiz) Herman Müntz: A Mathematician's Odyssey,
*Mathematical Intelligencer***27**(2005), 22-31. [[pdf]]. Review from Zentralblatt. - Density in Approximation Theory,
*Surveys in Approximation Theory***1**(2005), 1-45. [[pdf], [ps]] and Surveys in Approximation Theory. Review from MR. Review from Zentralblatt. - Strictly Hermitian Positive Definite
Functions,
*Journal d'Analyse Math.***94**(2004), 293-318. [[pdf]]. - Interpolation by Matrices,
*Electronic Journal in Linear Algebra***11**(2004), 281-291. [[pdf]]. This article may be viewed directly from ELA. Review from Zentralblatt - Density Methods and Results in Approximation Theory,
*Orlicz Centenary Volume, Banach Center Publications, Volume 64*, Z. Ciesielski, A. Pelczynski, L. Skrzypczak (eds.), 173-192, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2004. [[pdf]]. - Strictly Positive Definite Functions on a Real
Inner Product Space,
*Advances in Computational Mathematics***20**(2004), 263-271. [[pdf]]. This article may be viewed at Springer. Review from MR. - (with C. de Boor) The B-spline Recurrence Relations
of Chakalov and Popoviciu,
*Journal of Approximation Theory***124**(2003), 115-123. [[pdf]]. This article may be viewed at Science Direct. Review from Zentralblatt. -
Negative Theorems in Approximation Theory,
*American Math. Monthly***110**(2003), 900-911. [[pdf]]. Some corrections regarding this paper are in this file. This paper is available from JSTOR. Review from MR. Review from Zentralblatt. - (with A. Atzmon) Rank Restricting Functions,
*Linear Algebra and its Applications***372**(2003), 305-323. [[pdf]]. This article may be viewed at Science Direct. Review from Zentralblatt. - (with Uri Elias) Non-Linear Eigenvalue-Eigenvector
Problems for STP Matrices,
*Proceedings of the Royal Society of Edinburgh: Section A***132**(2002), 1307-1331. [[pdf]]. See Cambridge journals. Reviews from Zentralblatt and from MR. - (with Uri Elias) Non-Linear Eigenvalue Problems for a Class of
Ordinary Differential Equations,
*Proceedings of the Royal Society of Edinburgh: Section A***132**(2002), 1333-1359. [[pdf]]. See Cambridge journals. Reviews from Zentralblatt and from MR. - Some Remarks on Zero-Increasing
Transformations,
*Approximation Theory X: Abstract and Classical Analysis*, C. K. Chui, L. L. Schumaker, J. Stoeckler (eds.), 333-352, Vanderbilt Univ. Press., Nashville, 2002. [[pdf]]. Review from MR. - (with J. M. Carnicer and J. M. Pena) On some Zero-Increasing
Operators,
*Acta Math. Hungar.***94**(2002), 173-190. [[pdf]]. Reviews from Zentralblatt and from MR. - (with J. M. Carnicer and J. M. Pena) On Zero-Preserving Linear
Transformations,
*Journal of Mathematical Analysis and Applications***266**(2002), 237-258. [[pdf]]. This article may be viewed at Science Direct. - Weierstrass and Approximation Theory,
*Journal of Approximation Theory***107**(2000), 1-66. [[pdf]]. This article may be viewed at Science Direct. Some additions/corrections regarding this paper are in this file. Reviews from Zentralblatt and from MR. - On a Problem of G. G. Lorentz,
*Journal of Approximation Theory***103**(2000), 29-54. [[pdf]]. This article may be viewed at Science Direct. Some additional comments on this paper are here. Reviews from Zentralblatt and from MR. - Approximation Theory of the MLP Model in Neural Networks,
*Acta Numerica***8**(1999), 143-196. [[pdf]]. This article may be viewed at Cambridge Online. Review from MR. - (with Vitaly Maiorov)
Lower Bounds for Approximation by MLP Neural Networks,
*Neurocomputing***25**(1999), 81-91. [[pdf]]. This article may be viewed at Science Direct. - (with Martin D. Buhmann)
Identifying Linear Combinations of Ridge Functions,
*Adv. in Applied Math.***22**(1999), 103-118. [[pdf]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR. - An Interlacing Property of Eigenvalues of Strictly Totally Positive
Matrices,
*Linear Algebra and its Applications***279**(1998), 201-206. [[pdf]]. This article may be viewed at Science Direct. Review from MR. - Uniqueness of Smoothest Interpolants,
*East Journal of Approximation***3**(1997), 377-380. [[pdf]]. Review from Zentralblatt. - Approximating by Ridge Functions, in
*Surface Fitting and Multiresolution Methods*, A. Le Mehaute, C. Rabut, L. L. Schumaker (eds.), pp. 279-292, Vanderbilt University press, Nashville, 1997. [[pdf]]. Review from MR. - (with Oleg Davydov)
Best Approximation and Cyclic Variation Diminishing Kernels,
*Journal of Approximation Theory***89**(1997), 380-423. [[pdf]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR. - (with Martin Buhmann) On a Recovery Problem,
*Annals of Numerical Mathematics***4**(1997), 129-142. The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin. [[pdf]]. Reviews from Zentralblatt and from MR. -
TDI-Subspaces of
*C(R*and Some Density Problems from Neural Networks,^{d})*Journal of Approximation Theory***85**(1996), 269-287. [[pdf]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR. - Spectral Properties of Totally Positive Kernels and Matrices,
in
*Total Positivity and its Applications*, M. Gasca, C. A. Micchelli (eds.), pp. 477-511, Kluwer Academic Publishers, 1996. [[pdf]]. - Some Density Problems in Multivariate Approximation, in
*Approximation Theory: Proceedings of the International Dortmund Meeting IDOMAT 95*, M. W. Muller, M. Felten, D. H. Mache (eds.), pp. 277-284, Akademie Verlag, 1995. [[pdf]]. Review from Zentralblatt. - (with B. Wajnryb)
A Problem of Approximation Using Multivariate Polynomials,
*Uspekhi Mat. Nauk***50**(1995), 89-110, (in Russian) =*Russian Math. Surveys***50**(1995), 319--340 (in English). [[pdf]]. Reviews from Zentralblatt and from MR. - (with B. Wajnryb)
Multivariate Polynomials: A Spanning Question,
*Constructive Approximation***11**(1995), 165-180. [[pdf]]. This paper may be viewed at Springer. Review from MR. - (with C. H. FitzGerald and C. A. Micchelli) Functions that
Preserve Families of Positive Semidefinite Matrices,
*Lin. Alg. and Appl.***221**(1995), 83-102. [[pdf]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR. - (with V. Ya. Lin) Approximation of
Multivariate Functions, in
*Advances in Computational Mathematics*, H. P. Dikshit, C. A. Micchelli (eds.), pp. 257-266, World Scientific, 1994. [[pdf]]. - (with C. A. Micchelli) Variational Problems Arising
from Balancing Several Error Criteria,
*Rendiconti di Matematica***14**(1994), 37-86. [[pdf]]. Reviews from Zentralblatt and from MR. - (with V. Ya. Lin) Fundamentality of
Ridge Functions,
*Journal of Approximation Theory***75**(1993), 295-311. [[pdf]]. This article may be viewed at Science Direct. Review from Zentralblatt. - (with D. Braess) Interpolation by Ridge Functions,
*Journal of Approximation Theory***73**(1993), 218-236. [[pdf]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR. - (with M. Leshno, V. Ya. Lin and S. Schocken) Multilayer
Feedforward Networks with a Non-Polynomial Activation Function can
Approximate any Function,
*Neural Networks***6**(1993), 861-867. [[pdf]]. This article may be viewed at Science Direct. - Uniqueness in Vector-Valued Approximation,
*Journal of Approximation Theory***73**(1993), 17-92. [[pdf]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR. - (with D. Wulbert) The Multi-Dimensional Van Neumann Alternating
Direction Search Algorithm in
*C(B)*and*L*,^{1}*Journal of Functional Analysis***104**(1992), 121-148. [[pdf]]. Reviews from Zentralblatt and from MR. - (with C. A. Micchelli) Descartes Systems from Corner Cutting,
*Constructive Approximation***7**(1991), 161-194. [[pdf]]. -
(with H. Strauss)
*L*–Approximation with Constraints,^{1}*Transactions of the American Mathematical Society***322**(1990), 239-261. [[pdf]]. This article may be viewed at JSTOR. Reviews from Zentralblatt and from MR. - (with L. Elsner and D. Hershkowitz) Functional Inequalities for
Spectral Radii of Non-Negative Matrices,
*Linear Algebra and its Applications***129**(1990), 103-130. [[pdf]]. Reviews from Zentralblatt and from MR. - (with C. A. Micchelli) Some remarks on nonnegative polynomials on
polyhedra.
*Probability, Statistics, and Mathematics: Papers in honor of Samuel Karlin*, 163-186, Academic Press, Boston, MA, 1989. [[pdf]]. Reviews from Zentralblatt and MR. - (with H. Strauss) Best Approximation with Coefficient Constraints,
*IMA Journal of Numerical Analysis***8**(1988), 1-22. [[pdf]]. Review from Zentralblatt. - (with B. Wajnryb) Necessary Conditions for Uniqueness in
*L*–Approximation,^{1}*Journal of Approximation Theory***53**(1988), 54-66. [[pdf]]. Reviews from Zentralblatt and MR. - Continuous Selections for the Metric
Projection on
*C*,_{1}*Constructive Approximation***4**(1988), 85-96. [[pdf]]. Reviews from Zentralblatt and MR. - On Smoothest Interpolants,
*SIAM Journal of Mathematical Analysis***19**(1988), 1431-1441. [[pdf]]. Review from MR. - (with H. Strauss) One-Sided
*L*–Approximation to Differentiable Functions,^{1}*Approximation Theory and its Applications***3**(1987), 81-96. [[pdf]]. Review from MR. - (with V. Totik) One-Sided
*L*–Approximation,^{1}*Canadian Mathematical Bulletin***29**(1986), 84-90. [[pdf]]. Reviewsfrom Zentralblatt and MR. - Unicity Subspaces in
*L*–Approximation,^{1}*Journal of Approximation Theory***48**(1986), 226-250. [[pdf]]. Review from MR. -
*n*-Widths and Optimal Recovery,*Proceedings of Symposia in Applied Mathematics*, Vol. 36, Ed., C. de Boor, 51-66, American Mathematics Society, Providence, 1986. [[pdf]]. - (with J. M. Anderson, P. Erdös and O. Shisha) The Closed
Linear Span of
{x
^{k}-c_{k}}_{1}^{∞},*Journal of Approximation Theory***43**(1985), 75-80. [[pdf]]. Reviews from Zentralblatt and MR. -
*n*–Widths of Sobolev Spaces in*L*,^{p}*Constructive Approximation***1**(1985), 15-62. [[pdf]]. Review from MR. - Some Extremal Problems for Strictly Totally
Positive Matrices,
*Linear Algebra and its Applications***64**(1985), 141-156. [[pdf]]. Reviews from Zentralblatt and MR. -
*n*-Widths in Approximation Theory: A Survey,*Approximation Theory IV*, Eds., C. K. Chui, L. L. Schumaker, J. D. Ward, 153-186, Academic press, N. Y., 1983. [[pdf]]. - (with G. J. O. Jameson) Positive and Minimal
Projections in Function Spaces,
*Journal of Approximation Theory***37**(1983), 182-195. [[pdf]]. Review from MR. - (with O. Shisha) A Variation on the Chebyshev Theory
of Best Approximation,
*Constructive Function Theory, 81*, 479-481, Sofia, 1983. [[pdf]]. Review from Zentralblatt. - (with C. de Boor and S. Friedland) Inverses of Infinite
Sign Regular Matrices,
*Transactions of the American Mathematics Society***274**(1982), 59-68. [[pdf]]. Review from MR. - (with C. de Boor) The Approximation of a Totally
Positive Band Matrix by Strictly Totally Positive One,
*Linear Algebra and its Applications***42**(1982), 81-98. [[pdf]]. - (with C. de Boor and R. Q. Jia)
Structure of Invertible (Bi)-infinite Totally Positive Matrices,
*Linear Algebra and its Applications***47**(1982), 41-55. [[pdf]]. - (with O. Shisha) Variations on the Chebyshev and
*L*Theories of Best Approximation,^{q}*Journal of Approximation Theory***35**(1982), 148-168. [[pdf]]. Reviews from Zentralblatt and MR. - Best Approximations by Smooth Functions,
*Journal of Approximation Theory***33**(1981), 147-178. [[pdf]]. Review from MR. - Bernstein's Comparison Theorem and a Problem of
Braess,
*Aequationes Mathematicae***23**(1981), 98-107. [[pdf]]. Reviews from Zentralblatt and MR. - (with C. A. Micchelli) On
*n*-Widths in*L*, II: Some related extremal problems,^{∞}*Constructive Function Theory, 77*, 403-416, Sofia, 1980. [[pdf]]. - (with L. Brutman) On the Erdos Conjecture concerning
Minimal Norm Interpolation on the Unit Circle,
*SIAM Journal of Numerical Analysis***17**(1980), 373-375. [[pdf]]. Review from MR. - (with Z. Ziegler) Interlacing Properties of the Zeros
of the Error Functions in Best
*L*Approximation,^{p}*Journal of Approximation Theory***27**(1979), 1-18. [[pdf]]. Review from MR. - On
*n*-Widths of Periodic Functions,*Journal d'Analyse Mathematique***35**(1979), 209-235. [[pdf]]. Review from MR. - Matrices and
*n*-Widths,*Linear Algebra and its Applications***27**(1979), 245-278. [[pdf]]. Review from MR. - (with C. A. Micchelli) The
*n*-Widths of Rank*n+1*Kernels,*Journal of Integral Equations***1**(1979), 111-130. [[pdf]]. - (with J. W. Lee) Spectral Properties and Oscillation
Theorems for Mixed Boundary-Value Problems of Sturm-Liouville Type,
*Journal of Differntial Equations***27**(1978), 190-213. [[pdf]]. Review from MR. - (with C. A. Micchelli) Some Problems in the
Approximation of Functions of Two Variables and
*n*-Widths of Integral Operators,*Journal of Approximation Theory***24**(1978), 51-77. [[pdf]]. Review from MR. - (with C. de Boor) Proof of the Conjecture of Bernstein
and Erdos concerning the Optimal Nodes for Polynomial Interpolation,
*Journal of Approximation Theory***24**(1978), 289-303. [[pdf]]. Review from MR. - Some Extremal Problems of Perfect Splines and
the Pointwise Landau Problem on the Finite Interval,
*Journal of Approximation Theory***23**(1978), 37-64. [[pdf]]. Review from MR. - (with C. A. Micchelli) Moment Theory for Weak Chebyshev Systems
with Applications to Monosplines, Quadrature Formulae and Best One-Sided
*L*Approximation by Spline Functions with Fixed Knots,^{1}*SIAM Journal of Mathematical Analysis***8**(1977), 206-230. [[pdf]]. Review from MR. - (with C. A. Micchelli) On
*n*-Widths in*L*,^{∞}*Transactions of the American Mathematics Society***234**(1977), 139-174. [[pdf]]. Review from MR. - (with C. A. Micchelli) Total Positivity and the Exact
*n*-Width of Certain Sets in*L*,^{1}*Pacific Journal of Mathematics***71**(1977), 499-515. [[pdf]]. Review from MR. - (with C. A. Micchelli) On a Best Estimator for the Class
*M*using only Function Values,^{r}*Indiana University Mathematics Journal***26**(1977), 751-759. [[pdf]]. Review from MR. - (with C. A. Micchelli) Best Mean Approximation to a 2-dimensional
Kernel by Tensor Products,
*Bulletin of the American Mathematical Society***83**(1977), 400-402. [[pdf]]. Review from MR. - (with C. de Boor) Backward Error Analysis for Totally Positive
Linear Systems,
*Numerische Mathematik***27**(1977), 485-490. [[pdf]]. Review from MR. - One-Sided
*L*-Approximation by Splines with Fixed Knots,^{1}*Journal of Approximation Theory***18**(1976), 130-135. [[pdf]]. - A Simple Proof of the Hobby-Rice Theorem,
*Proceedings of the American Mathematics Society***60**(1976), 82-84. [[pdf]]. Review from MR. - (with C. A. Micchelli) On
*n*-Widths and Optimal Recovery in*M*,^{r}*Approximation Theory, II*, Eds., G. G. Lorentz, C. K. Chui, L. L. Schumaker, 475-478, Academic Press, N. Y., 1976.[[pdf]]. Review from MR. - (with C. A. Micchelli) The Exact Asymptotic Value for the
*n*-Width of Smooth Functions in*L*,^{∞}*Approximation Theory, II*, Eds., G. G. Lorentz, C. K. Chui, L. L. Schumaker, 469-474, Academic Press, N. Y., 1976. [[pdf]]. Review from MR. - (with S. Karlin) Divided Differences and other
Non-linear Existence Problems at Extremal Points, in
*Studies in Spline Functions and Approximation Theory*, S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, 327-352, Academic Press, N. Y., 1976. [[pdf]]. - (with S. Karlin) Interpolation by Splines with Mixed Boundary
Conditions, in
*Studies in Spline Functions and Approximation Theory*, S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, 305-325, Academic Press, N. Y., 1976. [[pdf]]. - (with S. Karlin) An Extremal Problem of Multiple Gaussian Nodes, in
*Studies in Spline Functions and Approximation Theory*, S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, 143-162, Academic Press, N. Y., 1976.[[pdf]]. - (with S. Karlin) Gaussian Quadrature Formulae with Multiple Nodes,
in
*Studies in Spline Functions and Approximation Theory*, S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, 113-141, Academic Press, N. Y., 1976. [[pdf]]. - Applications of Representation Theorems to
problems of Chebyshev Approximation with Constraints, in
*Studies in Spline Functions and Approximation Theory*, S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, 83-111, Academic Press, N. Y., 1976. [[pdf]]. - Asymptotic Minimum Norm Quadrature Formulae,
*Numerische Mathematik***24**(1975), 163-175. [[pdf]]. - Representation Theorems for Tchebycheffian Polynomials with Boundary
Conditions and their
Applications,
*Israel Journal of Mathematics***17**(1974), 11-34. [[pdf]]. Review from MR. - (with S. Karlin) Oscillation Properties of Generalized
Characteristic Polynomials for
Totally Positive and Positive Definite Matrices,
*Linear Algebra and its Applications***8**(1974), 281-312. [[pdf]]. Review from MR.